High Energy Physics

One central property of the S-matrix is its invariance under field redefinitions. I will discuss how the geometry of field space makes this invariance manifest. This geometric formulation also has practical consequences. Scattering amplitudes and the renormalization group equations for a theory of scalars and gauge bosons only depend on geometric quantities. Also, the scattering amplitudes satisfy a geometric soft theorem.

Zoom link:  https://pitp.zoom.us/j/98973018515?pwd=MFJFSGM4RS9KRHFOREFBc1gvWXYwQT09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

Phase transitions in everyday systems are often catalysed by the presence of impurities, but in cosmology we typically assume the initial state is a homogeneous vacuum. In this talk I will discuss how topological defects can seed first order phase transitions in the early universe, causing them to proceed much more rapidly than in the usual case. The field profiles describing the decay do not have the typically assumed O(3)/O(4) symmetry, requiring an extension of the usual decay rate calculation. To numerically determine the saddle point solutions which describe the decay we use a new algorithm based on the mountain pass theorem. I will present results showing the significance of this effect for catalysis by magnetic monopoles in a simplified model, then discuss the same effect for domain walls catalysing the electroweak phase transition. The presence of domain walls can significantly modify the predictions for gravitational wave signal which may be observed with LISA.

Zoom link:  https://pitp.zoom.us/j/96182819088?pwd=cXhnVjFlT0tkc1VsRld0Yk43bFROUT09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

Recently, powerful quantum field theory techniques, originally developed to calculate observables in colliders, have been applied to describe classical observables relevant to gravitational wave physics. This has motivated a proliferation of approaches to extract classical information from quantum scattering amplitudes. Since the double copy suggests that the basis of the dynamics of general relativity is Yang-Mills theory,  in this talk I will first discuss scattering in Yang-Mills theory as a toy model to study the connection between the framework by Kosower-Maybee-O'Connell (KMOC), the language of effective field theory (EFT) and the eikonal phase. After a brief review of the KMOC formalism to compute classical observables from scattering amplitudes, I will consider the dynamics of colour-charged particle scattering and explain  how to compute the change of colour, and the radiation of colour, during a classical collision. Finally, moving on to gravity, I will discuss the deflection of light by a massive spinless/spinning object using the novel worldline quantum field theory (WQFT) formalism for classical scattering.

Zoom link:  https://pitp.zoom.us/j/98649931693?pwd=Z2s1MlZvSmFVNEFqdjk2dlZNRm9PQT09

I will speak about my recent work with Vladimir Kazakov where we study the SU(Nc) lattice Yang-Mills theory in the planar limit, at dimensions D=2,3,4, via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on the maximal length of loops, and the positivity conditions on certain correlation matrices. Our algorithm is inspired by the pioneering paper of P. Anderson and M. Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in the line with our previous work on matrix bootstrap. We thus obtain the rigorous upper and lower bounds on the plaquette average at various couplings and dimensions. The results are quickly improving with the increase of cutoff L. For D=4 and L=16, the lower bound data appear to be close to the Monte Carlo data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. We attempt to extract the information about the gluon condensate from this data. Our results suggest that this bootstrap approach can provide a tangible alternative to, so far uncontested, the Monte Carlo approach.

Zoom link:  https://pitp.zoom.us/j/96101268796?pwd=QkdJbm9GUzQ2YnIrM1NlcUt2Z3Nvdz09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

The background geometry seen by a propagating string in the non-relativistic limit is non-Lorentzian. This motivates us to study the non-relativistic AdS/CFT correspondence as a new example of non-AdS holography. In this talk I will focus on the string side of the correspondence, keeping an integrability perspective, and illustrate remarkable differences from the relativistic theory. I will report on recent progress made in AdS5xS5 non-relativistic strings, in particular regarding their classical string solutions, semi-classical expansion of the action, coset space formulation of the action, Lax pair and some preliminary progress on the spectral curve. Based on work done in collaboration with J. M. Nieto, O. Ohlsson Sax, A. Torrielli, S. Van Tongeren. 

Zoom link:  https://pitp.zoom.us/j/99895811528?pwd=YWIreWtzdmRBanpIZXBLLzY3ZFNoZz09

In this talk, I will describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced by Fortin and Skiba (DOI:10.1007/JHEP06(2020)028). To begin with, I will give some background on the formalism. In particular, I will map out how to build two-, three-, and four-point functions within this framework. I will then lay out how to construct tensorial generalizations of the well-known scalar four-point blocks for symmetric traceless exchange. As I will discuss, these generalized objects satisfy a number of contiguous relations. Together, these empower us to fully contract the four-point tensorial blocks, ultimately yielding finite spin-independent linear combinations of four-point scalar blocks potentially acted upon by first-order differential operators. I will next proceed to describe how to set up the conformal bootstrap equations directly in the embedding space. I will begin by mapping out a general strategy for counting the number of independent tensor structures, which leads to a simple path to generating the bootstrap equations. I will then examine how to implement this method to construct the two-point, three-point, and ultimately four-point conformal bootstrap equations. Lastly, I will illustrate this method in the context of a simple example.

Zoom link:  https://pitp.zoom.us/j/98920533892?pwd=cDQvOExJWnBsUWNpZml5S1cxb0FJQT09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

Direct detection experiments search for dark matter through its potential interactions with the SM particles. However, light dark matter models with particle masses below the GeV scale are still largely unconstrained. As we will see in this talk, sensitivity to such small momentum transfer can benefit from quantum sensors, which employ fundamental quantum mechanical phenomena to notice energy depositions otherwise unreachable. Quantum sensors can considerably extend the range in dark matter mass of traditional WIMP experiments and be complementary to other direct detection methods. In the first part of the talk, I will examine a proposal to use atom interferometers to detect a light dark matter subcomponent at sub-GeV masses. DM scattering off of one “arm” of the atom interferometer can cause trackable decoherence and phase shifts. Two key factors render atom interferometers highly competitive experiments for very low masses: they are sensitive to extremely low momentum deposition and their coherent atoms give them a boost in sensitivity. On the second part of the talk, I will present a new proposal to search for axions with optomechanical cavities.  As we will see, the Bose-enhancement of a final state coherent population of photons or phonons can help overcoming the strong suppression from the axion to photon coupling. A unique advantage of this novel search, axioptomechanics, is that the cavity size need no longer be matched to the axion mass, which allows to probe a wide window of axion masses.

Zoom Link:  https://pitp.zoom.us/j/92645586400?pwd=bm1VUEVqUzNOOXV2VnhEUkJtdWZrZz09